Machine learning for computational science and engineering最新文献

{"title":"LLM-driven design of physics-constrained constitutive models: Two agents are better than one.","authors":"Marius Tacke, Matthias Busch, Kian Abdolazizi, Jonas Eichinger, Kevin Linka, Roland Aydin, Christian Cyron","doi":"10.1007/s44379-026-00099-3","DOIUrl":"https://doi.org/10.1007/s44379-026-00099-3","url":null,"abstract":"<p><p>Developing constitutive models that capture how materials deform under load traditionally requires years of specialized expertise in continuum mechanics, machine learning, and scientific programming. Large language models (LLMs) have recently been shown to lower this barrier by generating constitutive models on demand, but existing single-agent pipelines lack systematic checks that the resulting models respect fundamental physical laws. To close this gap, we introduce the first multi-agent LLM-driven approach for constitutive model generation: a Creator agent proposes a model tailored to the data, while an Inspector agent critically audits each proposal against nine physical constraints and returns it for refinement whenever a violation is detected. We demonstrate this concept with constitutive artificial neural networks (CANNs) and benchmark it on brain tissue and rubber as isotropic materials, and on porcine skin tissue as a transversely isotropic material with a preferred fiber direction, using two different LLM backbones (Claude Opus 4.7 and Kimi K2.5). Whether a generated model satisfies the physical constraints is assessed numerically, by probing each constraint across a broad sample of deformation states, rotations, and perturbation directions. Adding the Inspector raises the share of exported models that pass all these checks from 90% to 95% for Opus and from 47% to 60% for Kimi. In addition, the generated models are on par with or even surpass expert-designed models in accuracy, extrapolate reliably beyond the training data, and generalize remarkably well to unseen loading paths. Separating generation from inspection thus turns LLM-driven constitutive modeling into a substantially more trustworthy process. The paradigm is deliberately technique-agnostic and scales automatically with advances in LLM capability, opening a promising path toward automated, physics-aware model discovery.</p>","PeriodicalId":521407,"journal":{"name":"Machine learning for computational science and engineering","volume":"2 2","pages":"51"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13630814/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149123930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"HKD-MGIN: a physics informed graph neural network using heat kernel diffusion for mapping adolescent functional brain connectivity.","authors":"B Patel, Z Habeeb","doi":"10.1007/s44379-025-00038-8","DOIUrl":"10.1007/s44379-025-00038-8","url":null,"abstract":"<p><p>Adolescence is a critical period characterized by dynamic changes in cognitive function and brain network organization. This study aims to model these complex neurodevelopmental processes using a novel graph-based learning framework that captures both local and global functional interactions across adolescent stages. We introduce the Heat Kernel Diffused Multi-task Graph Isomorphism Network (HKD-MGIN), which integrates multi-task functional magnetic resonance imaging (fMRI) data using heat kernel diffusion. This approach leverages a graph isomorphism network architecture to enable robust and interpretable representation learning. HKD-MGIN is applied to two predictive tasks: brain age estimation and sex classification. HKD-MGIN demonstrated strong performance in brain age estimation (RMSE = 1.864 ± 0.157; MAE = 1.492 ± 0.139; r = 0.816 ± 0.042) and achieved high accuracy in sex classification (ACC = 0.802 ± 0.015; AUC = 0.834 ± 0.017; F1 Score = 0.8199 ± 0.0514). Importantly, the model revealed functional circuits associated with cognitive maturation, highlighting its capacity for interpretability and neurobiological insight. These findings demonstrate the utility of heat kernel-based graph learning in modeling adolescent brain dynamics and identifying potential biomarkers of cognitive development. HKD-MGIN advances neuroimaging analysis by capturing hierarchical and distributed connectivity patterns, offering a promising direction for individualized tracking of neurodevelopmental trajectories.</p>","PeriodicalId":521407,"journal":{"name":"Machine learning for computational science and engineering","volume":"1 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13157510/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147877246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"From PINNs to PIKANs: recent advances in physics-informed machine learning.","authors":"Juan Diego Toscano, Vivek Oommen, Alan John Varghese, Zongren Zou, Nazanin Ahmadi Daryakenari, Chenxi Wu, George Em Karniadakis","doi":"10.1007/s44379-025-00015-1","DOIUrl":"10.1007/s44379-025-00015-1","url":null,"abstract":"<p><p>Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offeringa promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Finally, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.</p>","PeriodicalId":521407,"journal":{"name":"Machine learning for computational science and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13290273/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148321638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}